Rapidtables Root Calculator

Finding roots is a fundamental mathematical operation with applications in geometry, algebra, and many scientific fields. This calculator helps you quickly find square roots, cube roots, and nth roots of any number.

What is a Root Calculator?

A root calculator is an online tool that computes the roots of numbers. The most common roots are square roots (√x) and cube roots (∛x), but you can also find nth roots where n is any positive integer.

Roots are the inverse operation of raising a number to a power. For example, the square root of 9 is 3 because 3² = 9. Similarly, the cube root of 27 is 3 because 3³ = 27.

Note: For negative numbers, the root depends on the index. Even-indexed roots (like square roots) of negative numbers are not real numbers, while odd-indexed roots (like cube roots) can be negative.

How to Use This Calculator

Enter the number you want to find the root of in the "Number" field.
Select the root type (square, cube, or nth root).
For nth roots, enter the index n in the additional field that appears.
Click "Calculate" to see the result.
Use the "Reset" button to clear all fields.

The calculator will display the result in decimal form and show a chart visualizing the relationship between the number and its root.

Root Formulas

Square Root Formula:

√x = x^(1/2)

Cube Root Formula:

∛x = x^(1/3)

Nth Root Formula:

x^(1/n)

These formulas use exponentiation to calculate roots. The calculator implements these formulas using JavaScript's Math.pow() function.

Examples

Square Root Example

Find the square root of 16:

√16 = 16^(1/2) = 4

Cube Root Example

Find the cube root of 64:

∛64 = 64^(1/3) = 4

Nth Root Example

Find the 4th root of 16:

16^(1/4) = 2

FAQ

What is the difference between a square root and a cube root?: The square root of a number x is a value that, when multiplied by itself, gives x. The cube root of x is a value that, when multiplied by itself three times, gives x.
Can I find roots of negative numbers?: Yes, but only for odd-indexed roots (like cube roots). Even-indexed roots (like square roots) of negative numbers are not real numbers.
What is the difference between a root and an exponent?: A root is the inverse operation of an exponent. For example, the square root of 9 is 3 because 3 squared equals 9.
How accurate are the results from this calculator?: The calculator uses JavaScript's built-in Math.pow() function, which provides accurate results for most practical purposes.
Can I use this calculator for scientific calculations?: Yes, this calculator is suitable for basic mathematical operations and educational purposes.